A note on the one-step estimator for ultrahigh dimensionality

• Autores: Mingqiu Wang, Xiuli Wang, Xiaoguang Wang
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 260, Nº 1, 2014, págs. 91-98
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.09.037
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• Resumen

  • The one-step estimator, covering various penalty functions, enjoys the oracle property with a good initial estimator. The initial estimator can be chosen as the least squares estimator or maximum likelihood estimator in low-dimensional settings. However, it is not available in ultrahigh dimensionality. In this paper, we study the one-step estimator with the initial estimator being marginal ordinary least squares estimates in the ultrahigh linear model.

    Under some appropriate conditions, we show that the one-step estimator is selection consistent. Finite sample performance of the proposed procedure is assessed by Monte Carlo simulation studies.